{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Statistics - The Challenger Disaster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This ipynotebook is an excerpt of the excellent 'Bayesian Methods for Hackers'. For the whole book, check out http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/.\n",
    "\n",
    "Note that this Notebook requires the package *pymc*.\n",
    "\n",
    "author: Thomas Haslwanter, date: April-2020\n",
    "\n",
    "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temp (F), O-Ring failure?\n",
      "[[66.  0.]\n",
      " [70.  1.]\n",
      " [69.  0.]\n",
      " [68.  0.]\n",
      " [67.  0.]\n",
      " [72.  0.]\n",
      " [73.  0.]\n",
      " [70.  0.]\n",
      " [57.  1.]\n",
      " [63.  1.]\n",
      " [70.  1.]\n",
      " [78.  0.]\n",
      " [67.  0.]\n",
      " [53.  1.]\n",
      " [67.  0.]\n",
      " [75.  0.]\n",
      " [70.  0.]\n",
      " [81.  0.]\n",
      " [76.  0.]\n",
      " [79.  0.]\n",
      " [75.  1.]\n",
      " [76.  0.]\n",
      " [58.  1.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import seaborn as sns\n",
    "from urllib.request import urlopen\n",
    "\n",
    "url_base = 'https://raw.githubusercontent.com/thomas-haslwanter/statsintro_python/master/ipynb/Data/data_bayes/'\n",
    "inFile = 'challenger_data.csv'\n",
    "url = url_base + inFile\n",
    "challenger_data = np.genfromtxt(urlopen(url), skip_header=1, usecols=[1, 2],\n",
    "                                missing_values='NA', delimiter=',')\n",
    "# drop the NA values\n",
    "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n",
    "\n",
    "# plot it, as a function of tempature (the first column)\n",
    "print(\"Temp (F), O-Ring failure?\")\n",
    "print(challenger_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Defects of the Space Shuttle O-Rings vs temperature')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "sns.set_style('darkgrid')\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n",
    "            alpha=0.5)\n",
    "plt.yticks([0, 1])\n",
    "plt.ylabel(\"Damage Incident?\")\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks clear that the probability of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature t, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n",
    "\n",
    "We need a function of temperature, call it p(t), that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function*.\n",
    "\n",
    "\n",
    "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n",
    "\n",
    "In this model, the variable $\\beta$ that describes how quickly the function changes from 1 to 0, and $\\alpha$ indicates the location of this change. For example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2b95880bf48>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def logistic(x, beta, alpha=0):\n",
    "    return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n",
    "\n",
    "x = np.linspace(-4, 4, 100)\n",
    "\n",
    "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1, \\alpha = 0$\", ls=\"-\", lw=1)\n",
    "plt.plot(x, logistic(x, 3, 6), label=r\"$\\beta = 3, \\alpha = 6$\", ls=\"-\", lw=1)\n",
    "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5, \\alpha = 0$\", ls=\"--\", lw=1)\n",
    "\n",
    "plt.legend(loc='lower left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform the MCMC-simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "temperature = challenger_data[:, 0]\n",
    "D = challenger_data[:, 1]  # defect or not?\n",
    "\n",
    "# Define the prior distributions for alpha and beta\n",
    "# 'value' sets the start parameter for the simulation\n",
    "# The second parameter for the normal distributions is the \"precision\",\n",
    "# i.e. the inverse of the standard deviation\n",
    "\n",
    "# notice the`value` here. We explain why below.\n",
    "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n",
    "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n",
    "\n",
    "\n",
    "@pm.deterministic\n",
    "def p(t=temperature, alpha=alpha, beta=beta):\n",
    "    return 1.0 / (1. + np.exp(beta * t + alpha))\n",
    "\n",
    "# connect the probabilities in `p` with our observations through a\n",
    "# Bernoulli random variable.\n",
    "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n",
    "\n",
    "# Combine the values to a model\n",
    "model = pm.Model([observed, beta, alpha])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Programs\\WPy64-3760\\python-3.7.6.amd64\\lib\\site-packages\\pymc\\MCMC.py:81: UserWarning: Instantiating a Model object directly is deprecated. We recommend passing variables directly to the Model subclass.\n",
      "  warnings.warn(message)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 120000 of 120000 complete in 12.6 sec"
     ]
    }
   ],
   "source": [
    "# Perform the simulations\n",
    "map_ = pm.MAP(model)\n",
    "map_.fit()\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(120000, 100000, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the resulting posterior distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2b958fb8ec8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_samples = mcmc.trace('alpha')[:, None]  # best to make them 1d\n",
    "beta_samples = mcmc.trace('beta')[:, None]\n",
    "\n",
    "# histogram of the samples:\n",
    "plt.subplot(211)\n",
    "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
    "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
    "         label=r\"posterior of $\\beta$\", color=\"#7A68A6\", density=True)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
    "         label=r\"posterior of $\\alpha$\", color=\"#A60628\", density=True)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the probability curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'temperature')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw the probability as a function of time\n",
    "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n",
    "p_t = logistic(t.T, beta_samples, alpha_samples)\n",
    "\n",
    "mean_prob_t = p_t.mean(axis=0)\n",
    "\n",
    "plt.figure(figsize=(12.5, 4))\n",
    "\n",
    "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n",
    "of defect\")\n",
    "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n",
    "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n",
    "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
    "plt.title(\"Posterior expected value of probability of defect; \\\n",
    "plus realizations\")\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.xlim(t.min(), t.max())\n",
    "plt.ylabel(\"probability\")\n",
    "plt.xlabel(\"temperature\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Draw Confidence-Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Posterior probability estimates given temp. $t$')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats.mstats import mquantiles\n",
    "\n",
    "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n",
    "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n",
    "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n",
    "                 color=\"#7A68A6\")\n",
    "\n",
    "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n",
    "\n",
    "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n",
    "         label=\"average posterior \\nprobability of defect\")\n",
    "\n",
    "plt.xlim(t.min(), t.max())\n",
    "plt.ylim(-0.02, 1.02)\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
    "plt.xlabel(\"temp, $t$\")\n",
    "\n",
    "plt.ylabel(\"probability estimate\")\n",
    "plt.title(\"Posterior probability estimates given temp. $t$\")"
   ]
  }
 ],
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